Once I downloaded and extracted this older VNC client for Windows, I was ready to try again:

Once again I was prompted for the password:

After this I was greeted with the AmigaOne X1000 desktop on my Windows 7 PC, all colours correct! (Click to expand):

Below is the VNC client on the PC multitasking nicely with Office 2013 which I freshly installed this weekend on the PC to play around with (click to expand):

The screen update is not that fast from the X1000, but it is usable for common tasks. I wouldn't expect to play games remotely or anything like that!

Great result - I can now VNC to the X1000!

On the AmigaOne X1000, you can see the connection information from the verbose output of the program:

Next, of course I wanted to make AmiVNC4 run on boot so that I can connect to the X1000 anytime I want to from my PC without running the program from the Shell everytime. To do this I added some lines to the bottom of the System:s/user-startup file.

The relevant lines are highlighted while editing the file below in Notepad (Click to expand):

After a reboot I tested connecting from the PC and it worked! Excellent!

I hope this information is useful to anyone trying to get AmiVNC4 working on their X1000!